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OG17 OG18
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A city is hosting a table tennis tournament for its residents. Each team has exactly two players, and each player is on exactly one team. In each round, each team plays exactly one other team and either wins or loses. The winning team advances to the next round and the losing team is eliminated. No team or player drops out except by losing a game. The tournament is in progress, and exactly 512 players participated in the first round.From the available options, select a number of tournament rounds and a number of teams such that after the specified number of rounds there will be the specified number of teams remaining in the tournament. Make only two selections, one in each column.
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TPA
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For each values of y greater than $$2\sqrt3$$, the function f(x) is such that the equation f(x)=y has the form $$x=\frac{(y^2+12)}{y}$$.Select one value for a and one value for b such that the given information implies f(a)=b. make only two selections, one in each column.
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PREP07 Test 1
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 For the 5 days shown in the graph, how many kilowatt-hours greater was the median daily electricity use than the average (arithmetic mean) daily electricity use?
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PREP07 Test 1
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If xy = 1, what is the value of $$\frac{{2}^{(x+y)^2}}{{2}^{(x-y)^2}}$$ ?
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PREP07 Test 1
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Mary purchased 3 theater tickets with an average (arithmetic mean) price of $8. If Mary also purchases a fourth theater ticket with a price of $16, what is the average price of all 4 theater tickets?
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PREP07 Test 1
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Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?
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PREP07 Test 1
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 The table shows the number of shares of each of the 5 stocks owned by Mr. Sami. If Mr.Sami was to sell 20 shares of Stock X and buy 24 shares of Stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
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PREP07 Test 2
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A certain meter records voltage between 0 volts and 10 volts, inclusive. If the average (arithmetic mean) value of 3 recordings on the meter was 8 volts, what was the smallest possible recording, in volts?
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PREP07 Test 2
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If $$(400)(6,000) = (240)(100^x)$$, what is the value of x ?
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PREP07 Test 2
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A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost $300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers?
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Manhattan
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In a group of 9 children, there are twice as many girls as boys, and twice as many right-handed people as there are left-handed people. If a third of the boys are left-handed, how many girls are right-handed?
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Manhattan
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If n is an integer, f(n) = f(n – 1) – n, and f(4) = 10. What is the value of f(6)?
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Manhattan
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If 2 < 2x < 26, how many possible solutions for x are prime numbers?
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300难题
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Let n and k be positive integers with $$ k\leq n$$. From an n * n array of dots, a k * k array of dots is selected. The figure above shows two examples where the selected k * k array is enclosed in a square. How many pairs (n,k) are possible so that exactly 48 of the dots in the n * n array are NOT in the selected k * k array?
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300难题
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In the formula w=$$\frac{P}{\sqrt[t]{v}}$$, integers p and t are positive constants. If w = 2 when v = 1 and if w=1/2 when v = 64, then t =
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300难题
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A merchant purchased a jacket for $60 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant's gross profit on this sale?
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300难题
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An “Armstrong numbe” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and $$1^{3}+ 5^{3} + 3^{3}$$= 153. What is the digit k in the Armstrong number 1,6k 4 ?
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[test] - test - test - test - The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly $$\frac{1}{2}$$ centimeter thick.
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[test2] - The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly $$\frac{1}{2}$$
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OG21 OG2022
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The outer dimensions of a closed rectangular cardboard box are 8 centimeters by 10 centimeters by 12 centimeters, and the six sides of the box are uniformly $$\frac{1}{2}$$ centimeter thick. A closed canister in the shape of a right circular cylinder is to be placed inside the box so that it stands upright when the box rests on one of its sides. Of all such canisters that would fit, what is the outer radius, in centimeters, of the canister that occupies the maximum volume?
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